Question

What is the total compound interest of a loan for $5,000 with an annual interest rate of 8 percent at the end of a two-year period?


$832


$800


$400


$432

Answer 1

To calculate the total compound interest on a loan of $5,000 with an annual interest rate of 8% compounded annually over a period of 2 years, we can use the compound interest formula:

\[
A = P (1 + r)^n
\]

where:
- \( A \) is the total amount after n years,
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (decimal),
- \( n \) is the number of years the money is invested or borrowed.

In this case:
- \( P = 5000 \)
- \( r = 0.08 \)
- \( n = 2 \)

Substituting these values into the formula:

\[
A = 5000 (1 + 0.08)^2
\]

Calculating inside the parentheses first:

\[
1 + 0.08 = 1.08
\]

Now raising to the power of 2:

\[
A = 5000 (1.08)^2 = 5000 \times 1.1664 = 5832
\]

Now, we find the total compound interest by subtracting the principal from the total amount:

\[
\text{Compound Interest} = A - P = 5832 - 5000 = 832
\]

Thus, the total compound interest at the end of a two-year period is **$832**.